Re: Simple Sagnac

On Tue, 02 Aug 2005 21:32:21 -0700, bsr3997@xxxxxxxxxxx wrote:

>
> sal wrote:
>> Thanks for the informative response.
>>
>> On Sat, 30 Jul 2005 18:19:58 +0000, Daniel Cook wrote:
>>
[ snip ]
>
> Nice web page. A very clear simple explaination of the Sagnac
> effect. Just a few quibles.
>
> Your statement about the inability of Newtonian mechanics to explain
> Sagnac is backwards. Sagnac has often been used in this group in
> attempts to show that light travels at c+v or c-v in a moving frame.

Which just shows the level of silliness in some of the arguments in
this group.


> Why else would it take different times to go in opposit
> directions around the ring ;) To claim that the single clock is out
> of sync with itself is really grasping at straws. Some might even
> say that is absurd ;)

SR is intuitively unappealing. That's not news.


> Sagnac does not prove SR wrong because SR excludes rotations.

Untrue. Einstein's SR paper didn't treat acceleration, and
accelerated _observers_ are beyond the ability of SR to handle with
any grace, but accelerated _objects_ can be handled just fine in most
cases without stepping outside the math of SR. (If you want to be
nit-picky about it you need to add the "clocks postulate" to SR in
order to allow you to conclude anything about accelerated objects.)

And the reason Sagnac doesn't disprove SR is that SR predicts the
effect, and is, in that sense, confirmed by it, rather than
contradicted by it. To handle it strictly within the bounds of SR you
must look at it from the fixed frame, but from that point of view it's
a trivial bit of algebra to derive the effect.


> In "Relativity" Einstein wrote,
>
> "If, relative to K, K' is a uniformly moving co-ordinate system
> devoid of rotation, then natural phenomena run their course with
> respect to K' according to exactly the same general laws as with
> respect to K. This statement is called the principle of relativity
> (in the restricted sense)."
>
> The signal is partially dragged in media for both classical and
> relativistic models, as it must be to agree with experiment.

Right. Composition of velocities automatically gives partial
dragging. In aether theory partial dragging must be glued on somehow,
which is what Fresnel did, 'way back when. In ballistic theory it's
even harder to come up with a scenario in which partial dragging makes
sense.


> That is what Fizeau proposed and varified experimentally before SR
> existed. The media slows the signal to less than c, but slows it
> less when the media is moving in the same direction as the signal.
> The signal cannot be fully dragged or the signal speed could exceed
> c in the stationary frame with a fast moving media.

And that reasoning leads almost directly to the Lorentz transforms and
the composition of velocities formula, and suddenly you're looking at
what's commonly called "Lorentz ether theory" in this newsgroup; it
has been stated many times that its predictions are identical to those
of SR.

Since SR uses no "ether" one must conclude that this is another way to
say there is no evidence for the "ether" assumed by the so-called
Lorentz ether theory.


> One error I noticed in your classical view of the stationary frame
> is that you used 2pi r for the distance traveled by the signals.

No, I didn't. Equation (2) shows the time to go around clockwise,
given that the signal travels at velocity u(-) as viewed in the lab
frame to go around the ring that way. First line of (2):

u(-) t(-) = 2 pi r - v t(-)

Term by term:

u(-) is the signal speed going clockwise, viewed from fixed frame

t(-) is the time to go from the emitter to the detector

2 pi r is the full circumference of the ring

v t(-) is the distance traveled by the detector in that time

So the total distance traveled, as given in that equation, is

2 pi r - v t(-)

which is less than the full circumference. And t(-) is time to get
from the emitter to detector, not time to go all the way around the
circle. The detector is "coming to meet" the detector in that case.

Going the other way, it's given by equation (4), and is

2 pi r + v t(-)

and is, of course, longer than the full circumference, because the
detector is "running away" from the signal in that case.


> That is only true when there is no rotation. On the 28th Bilge
> wrote.
>
> "Why not? If the ring rotates with an angular velocity, w, then the
> light in the direction of rotation has to travel a distance:
>
>
> s = 2\pi r + wrt_1

Which is exactly what I said on that page. Bilge assumed k=u=c which
I did not, but aside from that it's the same formula.

Note that w = omega = angular velocity in the fixed frame, r = radius
in the fixed frame, and wr = v in my formula (2). Again, it's the
same formula.


> Where t is the time required for the light to reach the point on the
> ring that it started, since the ring rotated by a distance wrt in
> that time. Similarly, in the opposite direction, the distance
> traveled is s = 2\pi r - wrt_2. The speed of light in the ring is v
> = c/n, so it travels a distance s = vt_1 in the direction of
> rotation and s = vt_2 in the opposite direction."
>
> I'm sure the 2\pi is a typo for 2*pi.

No it certainly is not a typo. Bilge uses "\pi" to mean "the symbol
for pi" and juxtaposition of terms in an expression implies
multiplication, according to common modern usage. Bilge wrote what he
intended.


> The important thing here is that he included the wrt factor.

As did I.


> Leaving out the + or - wrt is what caused your time to come out the
> same in both directions.

No, it's not. It's assuming the signal moves at C/N relative to the
cable (rather than C relative to the fixed frame), combined with
vector addition of velocities, which leads to the time coming out the
same in both directions.


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